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Theory extraction in relational data analysis. (English) Zbl 1203.68195
de Swart, Harrie (ed.) et al., Theory and applications of relational structures as knowledge instruments. COST Action 274, TARSKI. Revised papers. Berlin: Springer (ISBN 3-540-20780-5/pbk). Lect. Notes Comput. Sci. 2929, 68-86 (2003).
Summary: From numerical mathematics we know that a linear equation \(Ax=b\) may be solved more efficiently if a reduction of \(A\) as \(A= \left( \begin{matrix} B & O \\ C & D\end{matrix}\right)\) is known beforehand. For the task \(\left(\begin{matrix} B & O\\ C & D\end{matrix}\right)\cdot \left(\begin{matrix} y\\ z\end{matrix}\right)= \left(\begin{matrix} c\\ d\end{matrix}\right)\), one will solve \(By=c\) first and then \(Dz=d-Cy\). Having an a priori knowledge of this kind is also an advantage in many other application fields. We here deal with a diversity of techniques to decompose relations according to some criteria and embed these techniques in a common framework. The results of decompositions obtained may be used in decision making, but also as a support for teaching, as they often give visual help.
For the entire collection see [Zbl 1029.00017].
68T30 Knowledge representation
68W30 Symbolic computation and algebraic computation
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